{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T19:36:06Z","timestamp":1775244966638,"version":"3.50.1"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,11,11]],"date-time":"2022-11-11T00:00:00Z","timestamp":1668124800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,11,11]],"date-time":"2022-11-11T00:00:00Z","timestamp":1668124800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Oper. Res. Forum"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In the realm of dynamic demand, prosumers are agents that can produce and consume goods. In this paper, the problem we address involves a large population of prosumers and each prosumer has to decide if (s)he wants to produce or consume a certain amount of goods. The strategy of each agent depends on the average behavior of the population. We set the problem in a game-theoretic framework by modeling every prosumer as a player. For every player, a cost functional is designed to incentivize cooperation among the players. By taking the population size very large, a mean field game arises. The contributions of this paper are as follows. Firstly, we formulate the problem as first-order and second-order mean field games, the latter arises when we take stochastic disturbances into account. Secondly, mean field equilibria are derived by studying the corresponding linear-quadratic optimal control problem. Thirdly, results on stability of the first-order and second-order equilibria are established. A numerical study covering our findings concludes the paper.<\/jats:p>","DOI":"10.1007\/s43069-022-00164-6","type":"journal-article","created":{"date-parts":[[2022,11,11]],"date-time":"2022-11-11T11:02:32Z","timestamp":1668164552000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Mean Field Games on Prosumers"],"prefix":"10.1007","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8577-2346","authenticated-orcid":false,"given":"Wouter","family":"Baar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dario","family":"Bauso","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,11,11]]},"reference":[{"key":"164_CR1","doi-asserted-by":"crossref","unstructured":"Baar W, Bauso D (2019) Mean field games on prosumers. 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